Theorem eqvreleqi

Description: Equality theorem for equivalence relation, inference version. (Contributed by Peter Mazsa, 23-Sep-2021)

	Ref	Expression
Hypothesis	eqvreleqi.1	⊢ 𝑅 = 𝑆
Assertion	eqvreleqi	⊢ ( EqvRel 𝑅 ↔ EqvRel 𝑆 )

Proof

Step	Hyp	Ref	Expression
1		eqvreleqi.1	⊢ 𝑅 = 𝑆
2		eqvreleq	⊢ ( 𝑅 = 𝑆 → ( EqvRel 𝑅 ↔ EqvRel 𝑆 ) )
3	1 2	ax-mp	⊢ ( EqvRel 𝑅 ↔ EqvRel 𝑆 )